Dynamic visual scenes present an observer with motion contours that indicate the location of the boundaries of moving objects. Because motion contours are useful for figure-ground discrimination and for the analysis of depth structure, their fast and accurate identification is ecologically significant. Visibility depends on the difference between motion vectors on either side of the contour, each of which has a speed and a direction. The relative contribution of speed and direction in determining the visibility of a motion-defined contour can provide important clues about the neural mechanisms underlying the perception of motion discontinuities. Here, we explore the computational requirements of detecting motion contours for stimuli that we previously investigated with psychophysical methods in a study which found that speed and direction are detected independently by human observers and combined such as to optimise perceptual performance (Durant and Zanker 2008, Vision Research 48, 1053–1060). We simulate the detection of motion contours by computing local motion signals using correlation detectors and deriving global motion patterns from the local signal distributions. From histograms of local motion signals, clusters corresponding to different regions of uniform motion are identified. The clusters are used to group local motion signals in order to segment the images and identify contours. This process is based on a hierarchical structure with forward and backward connectivity computing an initial local detection, then computing global motion to support a subsequent segmentation. The reliability of separating clusters attributable to the different stimulus regions is used as an indicator of the visibility of the contours. In computer simulations, we find that differences in direction are more reliably detected than differences in speed. We discuss this result and the general structure of the model in relation to the previous psychophysical findings.